The evolution x-ray computed tomography (CT) has produced scanners with decreasing data acquisition and image reconstruction times and improved density and spatial resolutions. The improvements have been achieved primarily by the use of more sophisticated data acquisition systems and faster image reconstruction hardware. The image quality has also been improved by reevaluating assumptions used in the algorithms of the early generations of CT scanners and by incorporating corrections and/or refinements of these assumptions within the image reconstruction algorithm.
The assumptions were initially made to assure the compatability of the real data collected by an actual scanner with theoretical reconstruction algorithms which for example require an infinite number of line-integral values of the two-dimensional attenuation function. In reconstruction algorithms, the line-integral values are inverted resulting in two-dimensional object density functions which are presented to the user as images.
CT scanners employ a plurality of source means and a plurality of detector means which are each provided with a scanning movement, relative to a body, to provide a measure of attenuation for each of a plurality of straight line radiation connecting the source means to the detector means. Those attenuation measurements are then processed by suitable means to provide a distribution of line-integral values of object density function. To provide the required plurality of line-integrals, the source and detectors are moved in predefined patterns.
In a translate-rotate system, assuming the source emits a fan-beam formed of a plurality of pencil beams, the detectors, during translation, provide information relevant to a plurality of sets of parallel beam paths. The sets are angularly spaced by the angular separation of the beams. Each pencil beam, in the course of the lateral scan, provides the data for a set of parallel beam paths. Data from each such parallel set is processed to give parallel projections of the object density function. Usually, filtered backprojection methods are used to reconstruct the density function from the parallel projections collected over a minimum of 180 degrees of rotation.
In rotate-rotate scanners, in which the source and detectors are fixed in relation to one another and rotate together around the object, it is customary to convert the non-parallelized data collected thereby into parallel data format by a suitable resorting or re-binning technique. This is because conventional backprojection methods are adapted to the parallelized data produced by a translate-rotate type scanner. Re-binning or resorting techniques have been disclosed in the U.S. Pat. No. 4,266,136. The resorting algorithm requires a rotation angle of 180 degrees plus the angle subtended by the source-fan. Methods are also available for directly reconstructing the fan-beam data required by the resorting algorithm. This method is outlined in the paper: D. L. Parker, "Optimal Short Scan Convolution Reconstruction for Fanbeam CT," Medical Physics, Vol. 9, No. 2, March 1982, pp. 254-258.
Most of the presently available CT scanners use what can be referred to as coplanar source-detector configurations. That is, the centers of apertures of all the detector- and the source-positions are in the same plane known as the scan plane. This two-dimensional configuration is the result of the mathematics of conventional reconstruction theory that require all line-integrals of the density function to lie in a plane.
A major problem with actual CT scanners is that the detector and source means have apertures that extend in the axial direction; i.e., perpendicular to the scan plane. Implicit to the image reconstruction algorithm is the assumption that the object is spatially invariant in the axial direction. This assumption is seldom satisfied. Thus, what are known as "partial volume" artifacts are present in the final reconstruction of the scan plane. In order to reduce partial volume artifacts, the heights of the source and detector apertures in the axial direction are made as small as possible.
In some CT scanners the source and the detector apertures are intentionally designed to be in separate planes. Such machines are described as having noncoplanar configurations. Noncoplanar machines have been described in the following articles: D. P. Boyd, "Theoretical Possibilities for CT Scanner Development," Diagnostic Imaging, Dec. 1982; R. A. Robb, "X-ray Computed Tomography: An Engineering Synthesis of Multiscientific Principles," in "Critical Reviews in Biomedical Engineering," Ed. J. R. Bourne, CRC Press, March 1982, pp. 265-327. A consequence of this new noncoplanar geometry is that the partial volume artifacts will be enhanced. This new level of partial volume artifacts are denoted as "noncoplanarity artifacts".
Noncoplanarity causes several different types of artifacts of which two are of primary concern. The first is related to axial resolution and the other is related to inconsistencies in the data interacting with the reconstruction algorithm.
The slice-volume of a scanner is the volume formed by the collection of all of the paths taken by the line-integral values. The slice-volume in the noncoplanar geometry is much larger and more irregular than the slice-volume in the coplanar geometry. Because objects have spatial variations in the axial direction, the axial resolutions of noncoplanar machines are significantly less than in corresponding coplanar scanners.
The second type of artifact caused by noncoplanarity is a result of inconsistencies in the measured line integral data. All present reconstruction algorithms assume or require that line integrals along two opposite paths be identical. However, if there is any variation of the object's attenuation coefficient in the axial direction, the line-integrals along the two opposite paths in the noncoplanar configuration will not be identical. The effect of this inconsistency is to cause artifacts in reconstructed images. Because of the physical shape and density distribution of the artifacts, they are called "butterfly artifacts."
If scanners with noncoplanar geometries are ever expected to produce valuable images, the large slice volume and the "butterfly artifacts" must be reduced. Since there always exists a degree of noncoplanarity, there is always a point at which the noncoplanarity artifacts will make the images clinically unusable. Thus, there exists the need for systems and methods to correct for noncoplanarity artifacts.